Finite Group Databasebeta

← #34059572

Subgroups — #34059572

Order 19072.

246 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750596C211yesmaximal, characteristic
2C4×C22⋊#10597010C211yesmaximal, characteristic
3#23749472C211yesmaximal, characteristic
4C2×#14558746C412yescomplemented
5C2×C22⋊#10597010—21no—
6C2×C4×#10597010—21no—
7#18011968—21no—
8C22⋊#11924753—21no—
9(C2×#10597010)⋊C4C412yescomplemented
10C22×C4×D149C2211yescharacteristic
11C2×#14558713—21no—
12C2×C4×Dic149—21no—
13#18011818C411yescharacteristic, complemented
14#95×C149C411yescharacteristic, complemented
15C22×#10597010—22no—
16#14558746—42no—
17C2×#11924753—22no—
18C22⋊#10597010—22no—
19C22⋊#10597010—22no—
20C4×#10597010—42no—
21C23×D149D411yescharacteristic
22C22×Dic149—21no—
23C22×Dic149D411yescharacteristic
24C2×C4×D149—42no—
25C2×C4×D149C2×C411yescharacteristic
26C2×C4×D149C2×C411yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149Q811yescharacteristic
29#14558713—24no—
30C4×Dic149—42no—
31C22×C4×C149—21no—
32C22×C4×C149C2×C411yescharacteristic
33C2×#10597010—24no—
34C2×#10597010—42no—
35C2×#10597010—42no—
36#11924753—42no—
37C22×D149—21no—
38C22×D149—21no—
39C22×D149—22no—
40C22×D149—41no—
41C22×D149C22⋊C411yescharacteristic
42C22×D149C4⋊C411yescharacteristic
43C2×Dic149—22no—
44C2×Dic149—22no—
45C2×Dic149—41no—
46C2×Dic149—41no—
47C2×Dic149C22⋊C411yescharacteristic
48C2×Dic149C4⋊C411yescharacteristic
49C4×D149—22no—
50C4×D149—22no—
51C4×D149—41no—
52C4×D149—41no—
53C23×C149C22⋊C411yescharacteristic
54C2×C4×C149—22no—
55C2×C4×C149—41no—
56C2×C4×C149—41no—
57C2×C4×C149—41no—
58C2×C4×C149C4211yescharacteristic
59C2×C4×C149C4⋊C411yescharacteristic
60C22×C149—21no—
61C22×C149—21no—
62C22×C149#9511yescharacteristic
63C22×C149#10411yescharacteristic
64C22×C149#10411yescharacteristic
65C2×D149—21no—
66C2×D149—21no—
67C2×D149—21no—
68C2×D149—21no—
69C2×D149—21no—
70C2×D149—42no—
71C2×D149—42no—
72C2×D149#10412yes—
73#10597010—44no—
74C4×C149—21no—
75C4×C149—21no—
76C4×C149—42no—
77Dic149—21no—
78Dic149—42no—
79Dic149#9912yes—
80C2×C149—21no—
81C2×C149—21no—
82C2×C149#33911yescharacteristic
83C2×C149#33911yescharacteristic
84C2×C149#34211yescharacteristic
85D149—22no—
86D149—41no—
87C149#129711yescharacteristic, complemented, Sylow
88#1297—1491nomaximal, Sylow
89#407—1491no—
90C4×C22⋊C4—1491no—
91C4×C22⋊C4—1491no—
92C23×C4—1491no—
93C2×M16—1492no—
94C2×C22⋊C4—2981no—
95C2×C22⋊C4—2981no—
96C2×C42—2981no—
97C2×C42—2981no—
98C22⋊C8—2981no—
99C22⋊C8—2981no—
100#95—1492no—
101#95—1491no—
102#95#1059701011yescharacteristic, complemented
103C24—1491no—
104C22×C4—21no—
105C22×C4—2982no—
106C22×C4—2981no—
107C22×C4—5962no—
108C22×C4—1491no—
109C22×C4—1491no—
110C22×C4—1491no—
111C22×C4—1491no—
112C22×C4—1491no—
113C22×C4C2×#1059701011yescharacteristic
114M16—5962no—
115C2×C8—2982no—
116C22⋊C4—2984no—
117C22⋊C4—2982no—
118C22⋊C4—2982no—
119C42—5962no—
120C42—5962no—
121C23—2982no—
122C23—2981no—
123C23—2981no—
124C23—5961no—
125C23—1491no—
126C23—1491no—
127C23C22⋊#1059701011yescharacteristic
128C2×C4—22no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—2982no—
133C2×C4—2982no—
134C2×C4—2982no—
135C2×C4—2982no—
136C2×C4—2984no—
137C2×C4—5961no—
138C2×C4—5961no—
139C2×C4—5961no—
140C2×C4—5962no—
141C2×C4—5962no—
142C2×C4—5961no—
143C2×C4—1491no—
144C2×C4—1491no—
145C2×C4C4×#1059701011yescharacteristic
146C2×C4C4⋊#1059701011yescharacteristic
147C8—5962no—
148C22—21no—
149C22—21no—
150C22—2981no—
151C22—2981no—
152C22—2981no—
153C22—2981no—
154C22—2981no—
155C22—5962no—
156C22—5962no—
157C22—1492no—
158C22(C2×#10597010)⋊C411yescharacteristic
159C22#1801197511yescharacteristic
160C22#1801197611yescharacteristic
161C4—21no—
162C4—21no—
163C4—42no—
164C4—2981no—
165C4—5962no—
166C4—5964no—
167C4—1492no—
168C2—21no—
169C2—21no—
170C2—2982no—
171C2—5961no—
172C2#2375049511yescharacteristic
173C2#2375049611yescharacteristic
174C2#2375050211yescharacteristic
subgroupG/H
centerC22(C2×#10597010)⋊C4
commutatorC2×C4×C149C42
FrattiniC22×C4C2×#10597010
Fitting#95×C149C4
socleC22×C149#95
prime radicalC23×D149D4
cosocleC22×C4×D149C22
hypercenter#95#10597010
hypocenterC149#1297
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×#14558746C4semidirect
9. (C2×#10597010)⋊C4C4semidirect
13. #18011818C4semidirect
14. #95×C149C4semidirect
87. C149#1297semidirect
102. #95#10597010semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237505962
C4×C22⋊#105970102
#237494722
#1297149